For any, for all, for each

Navigation is a precarious operation on the open sea. That is what makes the traditional methods of wave piloting used across the Marshall Islands so astonishing. Having little to no fixed landmarks for orientation, they use wave and wind patterns to orient themselves from island to island, piloting the subtle shifts in countervailing swells refracted by the contour of each atoll. To do this, they use a series of complex stick charts that position the boat in relation to land, current, and prevailing wind. This is used to draw hypothetical confluences between positions which operate as artificial guiding points within the patterns.  The maps themselves do not not account for the specific terrain of the Marshall Islands, instead the charts map possible geometries between the confluences of patterns that one could encounter over the course of navigation at any point in the open sea, rather than merely geometries that are known or accounted for1.

In a 1995 paper, anthropologist and mathematician Marcia Ascher highlights the peculiar abstractions that make the charts unique in one of the few mathematical accounts of the navigational practice. She not only extols the innovative manner in which these people surmounted the challenges of open sea navigation, she also hints at the profoundly different form of reasoning that underlies the process.  As opposed to what are deemed standard maps in many parts of the world, these charts were formulated in terms of mathematical models, not representations. What concerns us here for this paper relates to the rational affordances and political ramifications that result from this shift away from representation. That is, how they attempt to think of the power dynamic of epistemic regimes, with a particular focus on how knowledge is made operational and transferable in an equitable manner.

According to Ascher, the stick charts use generalized simplification to make complex patterns intelligible instead of merely representing them. They “strip[s] the system to what is considered essential […] phrased in terms of the geometric characteristics of the ocean phenomenon––the substance of the land and sea and wind are recast into points, lines, curves, and angles, and the interplay of the phenomena are recast into how these geometric aspects change and interact” (361, my italics)  By mapping the change and interaction instead of particular evidential objects, the “accumulated experiential knowledge has been conceptualized into a general system, a system that is believed to apply to oceans and land masses anywhere and everywhere” (Ascher 361). The model’s strength therefore is garnered not by the conveyance of accumulated knowledge, but rather by engendering a method for making the accumulated knowledge intelligible and reproducible across similar contexts. They propagate how one can correlate perception to knowledge that has been collected over time, making that knowledge operational.

To assess these subtle movements in gradation and pattern, navigators are trained in a series of perceptual techniques. By laying flat on the hull of the boat, for instance, or by free floating in water, practitioners may learn to sense the specific shifts in pattern that would provide a perceptual account of a voyage with regard to the geometries of the charts (Ascher 361). In this sense, the navigator interprets the charts within the context, purpose and social milieu of the knowledge accumulation; discerning general abstract geometries in actual movements of the current and wind. Successful interpretation is reliant on their ability to translate sensory accounts into informational techniques within the framework of the model as opposed to essentially determining specific locational markers. Active, situated interpretation correlates reality with a rationalized account of that reality within a collectivized heuristic2.

Abstractions formed in relation to material anchors, thereby, hold together the most essential qualities of the chart’s functionality. The only specificities needed in the use of the model are that of the dominant wind direction, general current flows, and the position of the boat itself. From there, the navigator need only identify the various confluences of pattern change in order to orient toward a desired path. Even more striking is the fact that these objects are not actually carried on the voyages. They are left at home, hidden away as a sacred object, only taken out for study while on land. Similarly, they are many. As the charts provide only conditional information about the seascape, each chart, each general geometric possible, is equivalent so long as it adequately frames a consistent branching of possibles, thus accounting for the variety and number of charts that exist. This fact would suggest that the devices are used to transmit and preserve knowledge rather than be knowledge (Acher 362). This seems to be compounded by the mnemonic devices and songs used to help the navigators remember the discrete formulations while at sea, ritualizing the perceptual techniques so as to commit their principles to memory while, subsequently, maintaining confidence and alertness in the navigator whose technical expertise is relied on by his co-voyagers (Ascher 364). Of course the realizability of the specific navigator is always at stake, but the collective maintenance of transmission allows the cognitive image of knowledge to be stored in method instead of detail, streamlining the purpose, the voyage, and the determination that gives such generalized modes their effectivity.

Unlike representative maps, charts such as these operate as mathematical models. They parameterize the scalar and perspectival demands of generalized conditions and commitments to particularized forms of intelligibility. Alain Badiou, in his The Concept of Model, suggests that what distinguishes a model significantly from a representation lies in the fact that “the theory of models governs a dimension of the sciences’ practical immanence–a process, not only of the production of knowledge, but of the reproduction of the conditions of production”(44 original italics). He argues that this is the result of “the fragility of the distinction between the existence and the use of an experimental apparatus” being included in the overall translational potential of the model (44). In the case of the Marshallese charts, such variability is the charts’ most prescient strength. They map the movement of other tendencies in relation both to other elements and what is perceivable by humans aboard their own vessel. Mapping geometries as generalizations enables one to compress the nuance of multi-dimensional processes into a modelled space for possible navigational pathways one could take in any ocean, at any time, heading for any island. What they lack in the storage of particularized data about a nominal where, they make up for in demonstrating how to navigate.

Such a coordination of conditionals enables a form of “ampliative deductive reasoning” more commonly found in diagramming practices or other mathematical activity3. Extending accumulated knowledge, it makes components explicit, while also making the manner of explicit making operational for other use. Ampliative deduction, therefore, does not merely unpack causation and inference: it includes the methodology of its inference within the context of its deduction. It attends to the higher order reasoning realizing the manner of inference being used. The outcome is tied up with the logical commitments and parameters that justify and, to some degree, prove the validity of the deduction in reality. Amplification, therefore means offering what knowledge is being presented as a “power of knowing4” wherein the constitutive reasons for how inferences are correlated is made explicit enough to be repeated by someone else in another situation, where one would be able to use it to discover knowledge as it “pops up5” over the course of making it operational.

Key to this power of knowing is intelligibility and how it inculcates a perceptual and situated account within any knowledge, making it graspable and relevant to some aim. Yet, this production of intelligibility is often what is lacking in the presentation of knowledge except for the most specialised of the sciences and mathematics. Philosophy in particular often suffers from this type of presentation.
In a 2017 article entitled “The Place of Philosophy,” philosopher Danielle Macbeth describes how the “power of knowing” is seldom on offer in Western Philosophy, particularly as it tries to find its place within the broader ambit of knowledge production practices which have outpaced it in relation to logic (Mathematics) and evidentiary accounts about reality (Science). She states that in order to accommodate the advances in describing the world generated by scientific and mathematical innovations of the last centuries, or to even account for the pluralistic cultural norms of a global world, philosophy (specifically what could be termed Western or European Philosophy) must shift away from asking questions about what things are and into “questions about what it is to be human in the world in which we find ourselves” (982); from ontology alone to the intelligibility that produces conditional ontologies. This, for Macbeth, means dissociating the two historical projects that have been central to philosophy: a project concerning an absolute conception of reality, which has largely proved inadequate in the face of current scientific understanding, and a project concerning this same reality in question only “as it shows up in our everyday experience” (982) from the perspective of “natural truths” or, “truths that are the same for all rational beings with our biological form of life.” (9896). Intelligibility, for her, becomes the provenance of philosophy wherein the task of the discipline is to discover how human capacities of sensation and mind could grasp and produce the different dimensions of reality in a manner that is meaningful to human existence.

Yet, human forms of life have a tendency to trouble the capacities of mere biology. Our affordances for intelligibility are after all just as much a product of long form evolutionary adaptation of sense (biochemical reception mechanisms plus environment pressure plus cognitive signal development) as they are a product of language; not to mention other heuristic methods that coordinate instrumental interfaces capable of formalizing the activity of reason. This could also be said of other forms of life or forms of cognition. Thereby, the idea of a “natural truth” being conditioned on biological factors alone seems insufficient for describing the specific problem of intelligibility being posited here. This is perhaps why Macbeth qualifies this somewhat further in her monograph Realizing Reason where she states:

Truth is not a biological category. Nor is it a merely social category. Although we must begin with biological evolution through which living beings first emerge, that account must be supplemented with a further evolutionary process, the social evolution of creatures with characteristic practices, creatures able through their practices to institute the purely social significances that are involved in games. These purely social significances will then provide in turn a medium for the coalescence of the loci of authority that are the hallmark of the cognitive orientation on the world that is required for the pursuit of truth. As we will see, it is possible to be fully naturalistic (non-dualistic and non-magical) about our own cognitive and intellectual capacities, but only if we begin with life itself as the fruit of biological evolution, and then supplement that conception of life with the fruits of social, and ultimately intellectual, evolution as well. (27)

Whatever this truth consists of is poised upon artificial frameworks that are much more bound by semantic values than the contingencies of sensory capacities granted hominids over the long course of evolution. Which is not to say that it makes it less worthy of claims to producing effective means for reason-worthy intelligibility; quite the contrary. These conditioned and value-laden artificial systems instead afford a profound ability to craft sets of values in the shaping of human sensory and cognitive capacities insofar as they are explicitly constructed frameworks, meaning they are more often than not structured with the specific problem of cognition or intelligibility that it hopes to rationalize but within the bounds of normative objectives7. What remains then to be accounted for is how such truths have been transduced into heuristic methods that enable humans or other users to actively realize accumulated knowledge in reality, more often than not as technical systems.

This seems to be at the heart of what philosopher Patricia Reed has called a crisis of incompatibility wherein we have no existing means to “justly mitigate” the often conflicting social, economic, and ecological systems that shape our contemporary world (Reed). That is, the heuristic methods and models that have come to structure our technical world have made it nearly impossible to synthesize or string together the many perspectival and scalar demands that each of these systems hopes to ameliorate. She suggests that this practice could be described as a product of a battle over what the world is rather than what it could be; deduced from a series of constraints and commitments that are “given” as necessary and self-evidently intelligible; practices that hide their inferential logic behind a veil of necessity. It is a view that leads directly to a competitive battle between “perspectives ossiff[ied] into entrenched naturalizations of what is, confusing the accounting of a world with the world as such, like gazing an object from a single, particular position and insisting on consolidating that view with the object’s full dimensionality” (Reed).

Could the practices used for navigation in the Marshall Islands offer another type of model that would diminish this conflict? Afterall they construct problems in open-ended, hypothetical abstractions in a manner that generously shares their method of reasoning, offering it up to everyone and anyone willing to learn how to interpret them, while also orienting the activity of reason around intelligible heuristics rather than codified knowledge about what is. Therefore, what emerges from this model is an epistemic commitment to equity in the capacity to reason rather than a regulative equality of reason; that any and all who interpret the model are enabled by its “power of knowing” over and above what the former model could offer as simply equal in its comportment to provisional objectivity. Not just making it explicit, but also making it operational by formalizing a method for how this knowledge can be realized in reality.

The type of model made possible by the Marshall Island navigation charts represents a shift in structure which enables the principles of equity through its structure. It shows an alternative vision of how epistemic regions manage access, agency, and the power over who or what can make it operational.

How can such a model structure the inferential models used for social, economic and ecological systems that are in such dire need of revision? What would social or technical systems look like that are based on conditionals and requirements rather than regulation? Could and, more importantly, should this be a new, more constructive space for the activity of philosophy as a discipline? From the most foundational level, such a shift would entail modelling our understanding of reality as a space of what it could be rather than what it is – a subtle but poignant shift of model and heuristic method; one that coordinates perception to knowledge and sets conditions that are purposeful. A form of knowledge that is not simply cumulative and regulative but rather transformational with regards to our social cognitive, and political forms of life.

At its heart, this involves thinking about these social, political, and economic systems from the standpoint of what they require and what they satisfy with regards to criteria. There are, after all, many ways to satisfy requirements and criteria that lie outside what has been practiced or understood to be effective so far. That is, we needn’t think only in terms of that this or that typology of structure – as in a form of structure that is already known and schemetized – but rather thinking in terms of what it is that mechanisms in each of these different structures enables and how this could be provisionally coordinated with other structures. New patterns are waiting to be recognized, only we haven’t the means to triangulate them.

But this too is not quite enough. What needs to be attended to in this type of program is how human cognition and perception is wrapped up into the coordination process and, better yet, could be steered toward different forms of perception. Without that mapping between rationally inferred criteria and the perceptual accounts of how “to be human in the world in which we find ourselves,” there is little hope for making the mechanisms of said system grapsable or operational for most people. But this could go two ways: either adjusting systems to make them more graslable through different modes of known human perception or, more radically, attempt to shift the aperture of human perception toward new avenues no longer bound by biology alone. Arguably, this has been the aim of practices like philosophy and science throughout all civilizations and times. And as scientific and mathematical discovery soldier on, this aim can be pursued yet again both in the subtle accumulation of understanding techniques (the progressive accumulation of knowledge and understanding) just as in artificial practices and technologies that have explored each new frontier of those accumulations through abstraction and pattern recognition. Only now it is arguably the space for philosophy to find ways in which this process can evolve in a manner that justly and equitably bridges the many contributing knowledge practices and the humans that operate them: to point to what Charles Peirce once called an agapastic evolution of mind.

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Works Cited

Ascher, Marcia. “Models and Maps from the Marshall Islands: A Case in Ethnomathematics.” Historia Mathematica, vol. 22, 1995, pp. 347-370.

Badiou, Alain. The Concept of Model: An Introduction to the Materialist Epistemology of Mathematics. Translated and Edited by Zachary Luke Fraser and Tzuchien Tho. Re.Press, 2007.

Macbeth, Danielle. “The Place of Philosophy.” Philosophy East & West, vol. 67, no. 4, October 2017, pp. 966-985.

— Realizing Reason. A Narrative of Truth and Knowing. Oxford University Press, 2014.

Netz, Reviel. The Shaping of Deduction in Greek Mathematics. A Study in Cognitive History. Cambridge University Press, 2004.

Peirce, Charles S. “Evolutionary Love.” The Essential Writings of Charles Sanders Peirce. Edited by Edward C. Moore. Prometheus Books, 1998.

Reed, Patricia. “Xenophily and Computational Denaturalization.” e-flux Architecture, Artificial Labor, Sept. 18, 2017.  Accessed 30 Sept. 2017.

Simon, Herbert S.. The Sciences of the Artificial. Third Edition. MIT Press, 1996.

Tingley, Kim. “The Secrets of the Wave Pilots” New York Times. 17 March 2016. Accessed 3 May 2017.

The author would like to extend his sincere thanks to Ana Maria Guzman, Patricia Reed, and Anil Bawa Cavia whose comments and suggestions were essential to this paper.